Mapping Circles by a Linear Fractional Transformation

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A linear fractional transformation (or Möbius transformation) in the complex plane is a conformal mapping that has the form , where , , , and are complex, with . The transformation transforms circles in the plane into circles in the plane, where straight lines can be considered to be circles of infinite radius.


In this Demonstration, the red circle is transformed into the blue circle of the form .


Contributed by: Izidor Hafner (February 2016)
Open content licensed under CC BY-NC-SA



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